A137595 Binary terms such that duplicating the rightmost bit and counting repeats gives a palindrome.

1, 3, 6, 7, 13, 15, 25, 26, 28, 31, 49, 53, 59, 63

Offset

1,2

Comments

Decimal-binary representations of palindromic continued fractions.

Using the conversion rules, the first 14 fractions in the Stern-Brocot infinite Farey tree, (rational fractions k, 0 < k < 1) with palindromic continued fraction representations are: 1/2, 1/3, 2/5, 1/4, 3/8, 1/5, 5/12, 5/13, 3/10, 1/6, 7/16, 8/21, 4/15, 1/7.

Links

Table of n, a(n) for n=1..14.

Example

The first 14 binary terms corresponding to (1, 3, 6, 7, ...) = 1, 11, 110, 111, 1101, 1111, 1101, 11010, 11100, 11111, 110001, 110101, 111011, 111111, ...). 26 in binary is 11010. Appending an 0 to the right gives 110100. Recording the number of repeats, we get 2,1,1,2, a palindrome, so 26 is in the sequence. Later, we can obtain the fraction corresponding to continued fraction [2,1,1,2] = 5/13.

Crossrefs

Sequence in context: A088146 A176301 A191290 * A033053 A248388 A354765

Adjacent sequences: A137592 A137593 A137594 * A137596 A137597 A137598

Keyword

nonn,base

Author

Gary W. Adamson, Jan 29 2008

Extensions

Edited by Franklin T. Adams-Watters, Mar 29 2014

Status

approved